The currently increasing penetration of photovoltaic (PV) generation and electric vehicle (EV) charging in electricity distribution grids leads to higher system uncertainties. This makes it vital for load flow analyses to use probabilistic methods that take into account the uncertainty in both load and generation. Such probabilistic load flow (PLF) approaches typically involve three main components: (1) probability distribution models, (2) correlation models, and (3) PLF computations. In this review, state-of-the-art approaches to each of these components are discussed comprehensively, including suggestions of preferred modelling methods specifically for distribution systems with PV generation and EV charging. Research gaps that need to be explored are also identified. For further development of PLF analysis, improving input distribution modelling to be more physically realistic for load, PV generation, and EV charging is vital. Further correlation modelling efforts should focus on developing an effective spatio-temporal correlation model that is able to cope with high-dimensional inputs. The computational speed of PLF analysis needs to be improved to accommodate more complex distribution system models, and time-series approaches should be developed to meet operational needs. Furthermore, collection of higher-quality data is crucial for PLF studies, especially for improving the accuracy in the input variables.